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Spreading speeds and traveling waves for monotone systems of impulsive reaction-diffusion equations: Application to tree-grass interactions in fire-prone savannas

Banasiak Jacek, Dumont Yves, Yatat Djeumen Ivric Valaire. 2020. Spreading speeds and traveling waves for monotone systems of impulsive reaction-diffusion equations: Application to tree-grass interactions in fire-prone savannas. Differential Equations and Dynamical Systems, 34 p.

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Url - éditeur : https://rdcu.be/b7eeC

Abstract : Many systems in life sciences have been modeled by reaction–diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events, etc) such that an appropriate formalism like impulsive reaction–diffusion equations is necessary to analyze them. While several works tackled the issue of traveling waves for monotone reaction–diffusion equations and the computation of spreading speeds, very little has been done in the case of monotone impulsive reaction–diffusion equations. Based on vector-valued recursion equations theory, we aim to present in this paper results that address two main issues of monotone impulsive reaction–diffusion equations. Our first result deals with the existence of traveling waves for monotone systems of impulsive reaction–diffusion equations. Our second result tackles the computation of spreading speeds for monotone systems of impulsive reaction–diffusion equations. We apply our methodology to a planar system of impulsive reaction–diffusion equations that models tree–grass interactions in fire-prone savannas. Numerical simulations, including numerical approximations of spreading speeds, are finally provided in order to illustrate our theoretical results and support the discussion.

Mots-clés Agrovoc : Savane, Incendie spontané, Vitesse, Modélisation environnementale, Modèle mathématique, Interactions biologiques, Arbre, Herbage

Mots-clés complémentaires : interaction plante à plante

Mots-clés libres : Partial differential equation, Impulsive event, Monotone system, Recursive equation, Spreading speed, Traveling wave solution, Savanna, Pulse fire

Classification Agris : U10 - Computer science, mathematics and statistics
P40 - Meteorology and climatology

Champ stratégique Cirad : CTS 2 (2019-) - Transitions agroécologiques

Agence de financement hors UE : University of Pretoria

Auteurs et affiliations

  • Banasiak Jacek, University of Pretoria (ZAF)
  • Dumont Yves, CIRAD-BIOS-UMR AMAP (REU) ORCID: 0000-0003-4817-685X
  • Yatat Djeumen Ivric Valaire, University of Pretoria (ZAF) - auteur correspondant

Source : Cirad-Agritrop (https://agritrop.cirad.fr/596447/)

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